In the article [1]}, the stability is studied in the class
of models of derived type. At the free level, the wave operator of
the theory is given by a polynomial (characteristic polynomial) in
another formally self-adjoint operator of lower order. It has been
shown that each derived theory admits a series of conserved tensors,
which includes the canonical energy-momentum [2]}. The number
of entries in the series grows with the order of characteristic
polynomial. Even though the canonical energy is unbounded, the other
conserved tensors in the series can be bounded from below
[2]}. The bounded conserved quantity stabilizes the classical
dynamics of the theory. The quantum stability is explained by the
existence of the Lagrange anchor that relates a bounded conserved
quantity with the invariance of the model with respect to the time
translations.The concept of the Lagrange anchor has been
proposed in [4]} in the context of quantization of
non-Lagrangian field theories. Later, it has been recognized that
the Lagrange anchor connects symmetries and conserved quantities
[5]}. In the first-order formalism, the Lagrange anchor
defines the Poisson bracket [6]}. The Hamiltonian is given
by the conserved quantity in the series, being expressed in terms of
phase-space variables. The linear higher derivative theory is stable
if a bounded conserved quantity, being related to the
time-translation symmetry, is admitted by the model [1]}.
The articles [8]}, [9]} consider a problem of consistent
deformations of symmetries and conserved quantities that preserve
the stability of dynamics in the class of derived type models. In
all the cases interaction vertices do not come from the least action
principle with higher derivatives, but the equations of motion admit
the Hamiltonian form of dynamics. The main difficulty of the cited
above procedures is that they do not automatically preserve gauge
invariance. This restricts their applications in gauge systems.
